Have you seen this way of doing multiplication ?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
A collection of resources to support work on Factors and Multiples at Secondary level.
Explore the factors of the numbers which are written as 10101 in
different number bases. Prove that the numbers 10201, 11011 and
10101 are composite in any base.
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
Can you convince me of each of the following: If a square number is
multiplied by a square number the product is ALWAYS a square
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
Given the products of diagonally opposite cells - can you complete this Sudoku?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Given the products of adjacent cells, can you complete this Sudoku?
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A game in which players take it in turns to choose a number. Can you block your opponent?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
A game that tests your understanding of remainders.
Can you explain the strategy for winning this game with any target?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Can you work out what size grid you need to read our secret message?
Substitution and Transposition all in one! How fiendish can these codes get?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .
Can you find any perfect numbers? Read this article to find out more...
Explore the relationship between simple linear functions and their
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
What is the value of the digit A in the sum below: [3(230 + A)]^2 =